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So what we are going to do now is create a series of costs which are derived from the ones that we have. We are going to first find ourselves a family of average costs at various times, and what you’re going to be doing is taking sum of the cost functions, call it x, which are always going to be indexed on that volume index that’s right there, quantity, and you’re going to be dividing them by the quantity itself. So what you’re going to have is it’s going to breakdown to the total amount of this particular kind of cost divided by the quantity, which is going to give you a average of this kind of cost you have right here. So for example, if we go ahead and put fixed cost in the numerator, and so that’s just a fixed cost that’s there right away, which doesn’t change when the volume exchanges, divide it by q, you will have the fixed cost. That’s attributable to every single one of the units you produce. If you go ahead and take your variable cost, we will call it vc, index of the quantity divided by q, what you will have there is the variable cost per unit of output that you are producing. So again, once you know this definition of what an average cost is, you can generally know what all the other average costs are supposed to be. You could also create a total cost right here like that.

So let’s go ahead and give you what the shape of these things are, given the assumptions that we made on our extreme simplifying assumptions about our cost functions. We will start off with our fixed cost. now please note, that our total costs are shaped like this (draws a positive sloped linear graph), with the intercept of the fixed cost and the variable cost component up here having slope of alpha, so you can think of it as total cost is equal to fixed plus variable costs plus variable cost quantity times alpha. So there’s the definition that we will have for our cost that we will be using in class. If you are looking for the average fixed cost, so we call that AFC, just looking for this fixed cost component right there, the f, and dividing it by q. So you’re looking at a constant which is going to be divided by a quantity. You should see that this is a hyperbola, so you’re observing something like this (draws downward sloping hyperbola). So the quick description is suppose you have fixed costs of $10 and are producing one unit, you know that your average fixed cost is going to be $10. But if you have fixed costs of $10 and are producing 10 units your average fixed cost is going to be lower, it’s going to be $1. If you fixed cost is $10 and you’re producing a 100 units it’s going to be a 10th of a cent. So it’s a hyperbola and we are used to seeing it this way.

The next example we have is going to be something that’s called an average variable cost. What we are doing is taking that variable cost component, which is Q on alpha, and dividing it by q, and this is again our simplifications of cost, real costs don’t look like this, they look like something different. But you’re going to find out that average variable cost in our simplified model is just going to be a constant. So for us it will look like this (draws a linear graph with a horizontal line), always being alpha no matter what the particular volume is.

Now if you were to go up there and create the final cost function which is known as either average cost, or average total cost, one of the two. What you’re taking is these two components you have already created and adding them together. So you taking this fixed component, divided by the quantity, and what you’re doing is adding to it your variable component, dividing it by the quantity. So your average total cost should look like that (draws a hyperbola that starts above the horizontal line and slopes down toward it), while here is your average variable cost and your average fixed cost should be the vertical distance between the two. These are roughly the assumptions we have created out here next to the implications for the average cost, average fixed cost, and average variable cost defined for us. Now this will allow us to talk about how bad our assumption is because our assumption is actually a little on the nasty side, it doesn’t fit what is commonly observed about cost functions and cost functions are not as nearly as easy to deal with as your used to or would be led to believe.